The scope of this review is to provide a brief overview of the chemical applications carried out by local pair natural orbital coupled-electron pair and coupled-cluster methods. Benchmark tests reveal that these methods reproduce, with excellent accuracy, their canonical counterparts. At the same time, the speed up achieved by exploiting the locality of the electron correlation permits us to tackle chemical systems that, due to their size, would normally only be addressable with density functional theory. This review covers a broad variety of the chemical applications e.g. simulation of transition metal catalyzed reactions, estimation of weak interactions, and calculation of lattice properties in molecular crystals. This demonstrates that modern implementations of wavefunction-based correlated methods are playing an increasingly important role in applied computational chemistry.
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